A small ball is projected at an angle `alpha` with an initial velocity u between two vertical walls such that in the absence of the wall its range would have been `5d`. Given that all the collisions are perfectly elastic and distance between the walls be `d/2`, find.
(a) maximum height atained by the ball.
(b) total number of collisions with the walls before the ball comes back to the ground, and
(c) point at which the ball finally falls. The walls are supposed to be very tall.

Answer

A, B, C

Explanation

While colliding with the wall its vertical component `(v_y)` of velocity will remain unchanged (component along common tangent direction remains unchanged) while horizontal component `(v_x)` is reserved remaining same in magnitude. Thus, path of the particle will be as shown in figure.

(a) `H=(u^2sin^2alpha)/(2g)`
(b) Total number of collision with the walls before the ball comes back to the ground are nine.
(c) Ball will return to point O (the starting point)